When is something a "point object"?

I've gotten the question a bobzillion times since I did a show about angular momentum: 

I know you said angular momentum is L=Iw* for an extended object, and L=mvr for a point object.  But how do I tell whether something is an extended object or a point object?

* Yes, folks, I committed sacrilege - I wrote the variable for angular velocity not as a Greek omega, but as a Latin w.  And I've neither been struck by lightning, nor lost points on my AP exam.  

Consider the size of the object itself, and then consider the distance from the object's center to the axis of rotation.  If the distance to the axis of rotation is considerably bigger than the object's size, then you've got a point object.

A meterstick pivoted at one end? The distance from its center to the axis of rotation is 50 cm; the object length is 100 cm.  Not a point object.

The ball I shot at a wooden stick during the linked show? The ball was maybe 2 cm across.  The ball hit the stick about 9 cm below the stick's center, which was indicated as the axis of rotation for angular momentum conservation.  So we can consider the ball a point object in this case!

(That same ball rolling down a ramp, with the axis of rotation being the ball's center? That's gotta be treated as an extended object, because there is no distance at all between the ball's center and the rotational axis!)

What does r mean, then, in L=mvr? Isn't that the radius?

No, in the equation L=mvr for the angular momentum of a point object, r represents the "distance of closest approach" - extend the line of the object's motion, and find the closest that line gets to the axis of rotation.  That's r.

And how can something moving in a straight line have angular momentum, anyway?

If you're an AP physics 1 student: it just does.  L=mvr for a point object moving in a straight line.  That's, for now, simply a fact of physics.  If you're in AP physics C or above, you can ask for further detail in the comments, but only if you already understand the mathematics behind vector cross products.

No seriously!  One of the major obstacles to first-year students understanding physics is that they see the deep vector calculus reasoning behind some ideas, usually in a textbook or in wikipedia or from their teacher in response to the fastest student in the class... and they think they're supposed to understand every bit of the reasoning, they don't, and they lose confidence.  It's like trying to teach three different kinds of curve balls to a 10 year old pitcher, or the 1996 Chicago Bulls Triangle Offense to a middle school team.  Don't!  

For now, just use the L=mvr formula as a fact of physics.  You don't need to go any deeper than that for AP Physics 1!